Survival and stationary distribution of a stochastic facultative mutualism model with distributed delays and strong kernels

Qi, Ke; Liu, Zhijun; Wang, Lianwen; Wang, Qinglong

doi:10.3934/mbe.2021157

Cited by 8 publications

(1 citation statement)

References 44 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…32,33 The last one is considering the environmental noises that were proportional to the variables. 34 In the next section, we will first establish a deterministic HCV model (model (2.1)) and then extend it to a corresponding stochastic model (2.2) by adopting a relatively simple approach similar to Feng et al 34 Since persistence implies that disease will spread in the population and form endemic, extinction means that disease will not prevail or develop for long, and stationary distribution shows the stochastic statistical characteristic of the long time dynamical behaviors of the sample trajectories 35 ; we will focus on the above three main topics of models (2.1) and (2.2).…”

Section: Introductionmentioning

confidence: 99%

A nonlinear HCV model in deterministic and randomly fluctuating environments

Liu

Wang

et al. 2022

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

Two novel deterministic and stochastic nonlinear hepatitis C virus (HCV) models with nonlinear incidence rates as 𝛽S p E, 𝛽S p I, and 𝛽S p C q , containing acute and chronic infections, are developed, and an endeavor to understand their dynamics has been accomplished. For the former model, both the existence of unique equilibria and the sharp sufficient conditions of globally stable equilibria under different cases are established. Whereafter, the efforts taken to detect the asymptotic behaviors around equilibria, the existence of ergodic stationary distribution, and stochastic extinction of the latter model have been supplemented with meticulous theoretical proofs. At last, several numerical examples and discussions are illustrated to sustain and visualize our theoretical results. Compared and analyzed the numerical and theoretical results, we can find that the noise can influence the dynamics of disease and turn the disease from persistence to extinction. Moreover, several control measures are suggested based on our study.

show abstract